Dispersion of the Excitations of Fractional Quantum Hall States

Кукушкин, И. В.; Smet, J. H.; Scarola, V. W.; Umansky, V.; Klitzing, K. von

doi:10.1126/science.1171472

Cited by 124 publications

(119 citation statements)

References 25 publications

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“…In eq. (1.4), S 4 is the coefficient governing the low-momentum behavior of the projected structure factor [1]: 4 , where B is the magnetic length. Finally, in eq.…”

Section: Jhep01(2016)021mentioning

confidence: 99%

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Golkar

Nguyen

Son

2016

J. High Energ. Phys.

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We consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρ T (ω) andρ T (ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q 4 coefficient of the static structure factor S 4 , and the high-frequency shear modulus of the ground state µ ∞ , which is precisely defined. We confirm an inequality, first suggested by Haldane, that S 4 is bounded from below by |S − 1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin's absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.

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“…In eq. (1.4), S 4 is the coefficient governing the low-momentum behavior of the projected structure factor [1]: 4 , where B is the magnetic length. Finally, in eq.…”

Section: Jhep01(2016)021mentioning

confidence: 99%

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Golkar

Nguyen

Son

2016

J. High Energ. Phys.

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“…The neutral excitations are excitons of composite fermions 58,59,71,72 . The wave vector of the excitation is proportional to the distance between the excited composite fermion and the hole left behind.…”

Section: E Neutral Collective Modementioning

confidence: 99%

Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

Balram

Jain

2016

Phys. Rev. B

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The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this article that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Hall states. The rather weak dependence of the scale factor on the anisotropy provides insight into why fractional quantum Hall effect and composite fermions are quite robust to electron mass anisotropy. We discuss how better, though still approximate, wave functions can be obtained by introducing a variational parameter, following Haldane [Phys. Rev. Lett. 107, 116801 (2011)], but the resulting wave functions are not readily amenable to calculations. Our considerations are also applicable, with minimal modification, to the case where the dielectric function of the background material is anisotropic.

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“…It is possible to obtain very accurate numbers for many quantities of interest from the composite fermion (CF) theory [2][3][4] . Detailed comparisons have been carried out for activations gaps 5 , collective mode dispersions 6 , and spin-polarization phase transitions 3 . In all cases, the measured numbers are generally consistent with those predicted by theory, but the agreement is worse than that suggested by the accuracy of the theory as determined from comparisons with exact diagonalization results 3,[7][8][9] .…”

Section: Introductionmentioning

confidence: 99%

Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment

et al. 2015

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The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. We obtain accurate phase diagram for differently spin-polarized fractional quantum Hall states, and also estimate the effect of Landau level mixing using the modified interaction pseudopotentials given in the literature. We find that the observed phase diagram is in good quantitative agreement with theory that neglects Landau level mixing, but the agreement becomes significantly worse when Landau level mixing is incorporated assuming that the corrections to the energies are linear in the Landau level mixing parameter λ. This implies that a first order perturbation theory in λ is inadequate for the current experimental systems, for which λ is typically on the order of or greater than one. We also test the accuracy of the composite-fermion theory and find that it is very accurate for the states of the form n/(2n + 1) but for the states at n/(2n − 1) the results are sensitive to the lowest Landau level projection method. An earlier prediction of an absence of spin transitions for the n/(4n + 1) states is confirmed by more rigorous calculations, and new predictions are made regarding spin physics for the n/(4n − 1) states.

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Dispersion of the Excitations of Fractional Quantum Hall States

Cited by 124 publications

References 25 publications

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment

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